We study the resource investment decision faced by a firm that offers two demandclasses (i.e., products, services), while incorporating the firm's pricing decision into the investment decision. For this purpose, we consider a monopolistic situation and model the demand curve of each demand-class as a downward sloping linear function of its own price.The firm can invest in dedicated resources, which can only satisfy a specific demand-class, and/or in a more expensive, flexible resource, which can satisfy both demand-classes.We consider a two-stage stochastic decision model: In the first stage, the firm determines the dedicated and flexible resource capacities to invest in under demand uncertainty.In the second stage, demand curves are realized and the firm optimizes its revenue through pricing and resource allocation decisions, constrained by its capacity investment decision in the first stage.Our analysis provides the structure of the firm's optimal resource investment strategy as a function of price elasticities and investment costs, and shows how the value of resource flexibility depends on these parameters and demand correlations. Based on our analysis, we provide principles on the firm's optimal resource investment strategy under uncertainty.We show that it can be optimal for the firm to invest in the flexible resource when demand patterns are perfectly positively correlated, while it is not always optimal to invest in the flexible resource when demand patterns are perfectly negatively correlated.

Group testing (i.e., testing multiple subjects simultaneously with a single test) is essential for classifying a large population of subjects as positive or negative for a binary characteristic (e.g., presence of a disease). We study optimal group testing designs under subject-specific risk characteristics and imperfect tests, considering classification accuracy-, efficiency- and equity-based objectives, and characterize important structural properties of optimal testing designs. These properties allow us to model the testing design problems as partitioning problems, develop efficient algorithms, and derive insights on equity versus accuracy trade-off. One of our models reduces to a constrained shortest path problem, for a special case of which we develop a polynomial-time algorithm. We also show that determining an optimal risk-based Dorfman testing scheme that minimizes the expected number of tests is tractable, resolving an open conjecture. We demonstrate the value of optimal risk-based testing schemes with a case study of public health screening. This paper was accepted by Yinyu Ye, optimization.

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Flexible capacity has been shown to be very effective to hedge against forecast errors at the investment stage. In a make-to-order environment, this flexibility can also be used to hedge against variability in customer orders in the short term. For that purpose, production levels must be adjusted each period to match current demands, to give priority to the higher margin product, or to satisfy the closest customer. However, this will result in swings in production, inducing larger order variability at upstream suppliers and significantly higher component inventory levels at the manufacturer. Through a stylized two-plant, two-product capacitated manufacturing setting, we show that the performance of the system depends heavily on the allocation mechanism used to assign products to the available capacity. Although managers would be inclined to give priority to higher-margin products or to satisfy customers from their closest production site, these practices lead to greater swings in production, result in higher operational costs, and may reduce profits.resource flexibility, capacity allocation, supply chain performance, demand uncertainty, operational hedging

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Consider a set of product variants that are differentiated by some secondary attributes such as flavor, color, or size. The retailer's problem is to jointly determine the set of variants to include in her product line ("assortment"), together with their prices and inventory levels, so as to maximize her expected profit. We model the consumer choice process using a multinomial logit choice model and consider a newsvendor type inventory setting. We derive the structure of the optimal assortment for some important special cases, including the case of horizontally differentiated items, and propose a dominance relationship for the general case that simplifies the search for an optimal assortment. We also discuss structural properties of the optimal prices. Finally, motivated by our analytical results, we propose a heuristic solution procedure, which is shown to be quite effective through a numerical study.

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Abstract:We consider a container terminal discharging containers from a ship and locating them in the terminal yard. Each container has a number of potential locations in the yard where it can be stored. Containers are moved from the ship to the yard using a fleet of vehicles, each of which can carry one container at a time. The problem is to assign each container to a yard location and dispatch vehicles to the containers so as to minimize the time it takes to download all the containers from the ship. We show that the problem is NP-hard and develop a heuristic algorithm based on formulating the problem as an assignment problem. The effectiveness of the heuristic is analyzed from both worst-case and computational points of view.